Reduced cost numerical methods of sixth-order convergence for systems of nonlinear models

The objective of present study is to develop the iterative methods with higher convergence order but keeping the mathematical computations as small as possible. With this objective, two multi-step sixth order methods have been designed by utilizing only two Jacobian matrices and single matrix inversion apart from three functional evaluations. The techniques with these characteristics are rarely found in the literature. Comparing in the context of computational efficiency, both of the developed methods are exceptional, and outperform the existing methods. Numerical performance is analyzed by executing the experimentation on the selected nonlinear problems. Outcomes of the analysis are remarkable and significantly favor the new methods as compared to their existing counterparts, typically for large scale systems.